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Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-₁+ ₂y₁-2+ a₁0₁a-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5y-2 + a +0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y}. t 96 97 98 1 2 3 4 5 20 26 25 31 34 99 100 32 yt 27 34 29 28 a. Calculate the first four point estimates of {v}, i.e., ŷ1, ŷ2, ŷ3, and ŷ4. b. Given â100=20, calculate the forecast for future period 101 at time t = 100, i.e., 101 - ...

Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-₁+ ₂y₁-2+ a₁0₁a-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5y-2 + a +0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y}. t 96 97 98 1 2 3 4 5 20 26 25 31 34 99 100 32 yt 27 34 29 28 a. Calculate the first four point estimates of {v}, i.e., ŷ1, ŷ2, ŷ3, and ŷ4. b. Given â100=20, calculate the forecast for future period 101 at time t = 100, i.e., 101 - ...

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-1+ ₂Y₁-2+ a₁-0₁a₁-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5yt-2 +at+0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y₁}. t 1 2 3 4 5 96 97 98 99 100 Yt 20 26 25 31 34 27 34 29 28 32 a. Calculate the first four point estimates of {y}, i.e., ₁, 92, 93, and ŷ4. b. Given â 100=20, calculate the forecast for future period 101 at time t = 100, i.e., ŷ101.
Transcribed Image Text:Problem 10 A time series of 100 monthly observations was recorded and a time series analysis was conducted. The following ARMA(2,1) model has been fit to the time series, {y}: y₁ = ₁₁-1+ ₂Y₁-2+ a₁-0₁a₁-1 where a, is a random shock, distributed i.i.d. N(0,02). The solution to the model has been obtained as: y = 0.6y-1 - 0.5yt-2 +at+0.9a-1. Answer the following questions by considering the first and the last five values of the time series, {y₁}. t 1 2 3 4 5 96 97 98 99 100 Yt 20 26 25 31 34 27 34 29 28 32 a. Calculate the first four point estimates of {y}, i.e., ₁, 92, 93, and ŷ4. b. Given â 100=20, calculate the forecast for future period 101 at time t = 100, i.e., ŷ101.
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